Mauricio Pellegrino has insisted Southampton want to keep Virgil van Dijk and still sign another centre-back.
Saints are thought to be closing in on landing Lazio defender Wesley Hoedt for a fee of £15.5million.
St Mary's boss Pellegrino refused to rule out a move for the Holland centre-back, before claiming he would rather have too many defenders than not enough this season.
Wantaway Holland defender Van Dijk continues to agitate for a transfer before the end of the month, and will sit out Saturday's Premier League clash with West Ham.
Asked if he wants to add another centre-back to his squad even if Saints retain Van Dijk's services though, Pellegrino replied: "Yes, because as you know right now it's the position that we are in disadvantage.
"I think it's an area where we can improve with another player."
And when quizzed on whether five frontline centre-backs would be too many, Pellegrino continued: "I prefer to have a solution on the pitch, instead of problems on the pitch. I can mange that situation.
"Sometimes you have to make decisions as quickly as possible, because the competition will not wait for us."
Southampton remain confident of retaining Van Dijk's services past the end of the transfer window, despite the former Celtic man still trying to force his departure.
Saints could yet then add Lazio star Hoedt to their ranks, while also refusing to let Van Dijk leave.
When asked about Saints' pursuit of Hoedt, Pellegrino said: "I know the player but I will not talk about the market because when you talk about it, a negotiation isn't 80 per cent or 90 per cent, the negotiation is either 100 per cent or zero per cent.
"When he signs, a player is then for you (to talk about), but before that I have nothing to say."
Van Dijk missed Saints' goalless Premier League opener with Swansea on Saturday, officially due to a virus.
Pellegrino revealed the centre-back has now recovered - but will not be considered for selection for Saturday's home league clash with West Ham.
"The Virgil situation, nothing has changed, it's the same as last week," said Pellegrino, of Van Dijk.
"For that reason I have nothing to say on that. He's okay but he won't be available to play."
Southampton chairman Ralph Krueger this week backed plans for the England's summer transfer window to close before the start of next season.
And new Saints boss Pellegrino admitted he supports that position, adding: "I am in agreement with that.
"I would like to know our situation, and to keep all my players focused in our competition, in our responsibilities.
"Because to talk about the transfer market right now when we are competing, it's not good for the players and it's not good for us.
"At the end of a transfer window there is always a lot of movement. I would imagine in the next few days there will be movement because people will wait until the end to make good business. So I still expect deals to happen."